.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/vectors/glass_symmetry.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_vectors_glass_symmetry.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_vectors_glass_symmetry.py:


===========================
Glass Symmetry from Vectors
===========================

This example shows how to identify symmetry (in a glassy system but this could be useful other places)
by looking at the angles between 3 vectors in the diffraction pattern at some radial ring in k to identify
groups of 3 vectors that are subtended by the same angle.

This is a very simple example with more detailed examples to come.

.. GENERATED FROM PYTHON SOURCE LINES 12-18

.. code-block:: Python


    import pyxem as pxm
    from scipy.ndimage import gaussian_filter
    import matplotlib.pyplot as plt
    import numpy as np








.. GENERATED FROM PYTHON SOURCE LINES 19-20

First we load the data and do some basic processing

.. GENERATED FROM PYTHON SOURCE LINES 20-29

.. code-block:: Python

    s = pxm.data.pdnip_glass(allow_download=True)
    s.axes_manager.signal_axes[0].offset = -23.7
    s.axes_manager.signal_axes[1].offset = -19.3

    s.filter(gaussian_filter, sigma=(1, 1, 0, 0), inplace=True)  # only in real space
    s.template_match_disk(disk_r=5, subtract_min=False, inplace=True)

    vectors = s.get_diffraction_vectors(threshold_abs=0.5, min_distance=3)





.. rst-class:: sphx-glr-script-out

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.. GENERATED FROM PYTHON SOURCE LINES 30-31

Now we can convert to polar vectors

.. GENERATED FROM PYTHON SOURCE LINES 31-34

.. code-block:: Python


    pol = vectors.to_polar()





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.. GENERATED FROM PYTHON SOURCE LINES 35-37

This function gets the inscribed angle
accept_threshold is the maximum difference between the two angles subtended by the 3 vectors

.. GENERATED FROM PYTHON SOURCE LINES 37-60

.. code-block:: Python


    ins = pol.get_angles(min_angle=0.05, min_k=0.3, accept_threshold=0.1)

    flat_vect = ins.flatten_diffraction_vectors()

    fig, axs = plt.subplots()
    axs.hist(flat_vect.ivec["delta phi"].data, bins=60, range=(0, 2 * np.pi / 3))
    axs.set_xlabel("delta phi")
    axs.set_xticks(
        [0, np.pi / 5, np.pi / 4, 2 * np.pi / 5, np.pi / 2, np.pi / 3, 3 * np.pi / 5]
    )
    axs.set_xticklabels(
        [
            0,
            r"$\frac{\pi}{5}$",
            r"$\frac{\pi}{4}$",
            r"$\frac{2\pi}{5}$",
            r"$\frac{\pi}{2}$",
            r"$\frac{\pi}{3}$",
            r"$\frac{3\pi}{5}$",
        ]
    )




.. image-sg:: /examples/vectors/images/sphx_glr_glass_symmetry_001.png
   :alt: glass symmetry
   :srcset: /examples/vectors/images/sphx_glr_glass_symmetry_001.png
   :class: sphx-glr-single-img


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    [Text(0.0, 0, '0'), Text(0.6283185307179586, 0, '$\\frac{\\pi}{5}$'), Text(0.7853981633974483, 0, '$\\frac{\\pi}{4}$'), Text(1.2566370614359172, 0, '$\\frac{2\\pi}{5}$'), Text(1.5707963267948966, 0, '$\\frac{\\pi}{2}$'), Text(1.0471975511965976, 0, '$\\frac{\\pi}{3}$'), Text(1.8849555921538759, 0, '$\\frac{3\\pi}{5}$')]



.. GENERATED FROM PYTHON SOURCE LINES 61-62

cycle through colors in groups of 3 for each symmetry cluster

.. GENERATED FROM PYTHON SOURCE LINES 62-73

.. code-block:: Python


    points = ins.to_markers(
        color=["b", "b", "b", "g", "g", "g", "y", "y", "y", "r", "r", "r"]
    )
    original_points = vectors.to_markers(color="w", alpha=0.5)
    s.axes_manager.indices = (67, 55)  # jumping to a part with some symmetric structure

    s.plot(vmin=0.0)
    s.add_marker(points)
    s.add_marker(original_points)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/vectors/images/sphx_glr_glass_symmetry_002.png
         :alt: PdNiP Navigator
         :srcset: /examples/vectors/images/sphx_glr_glass_symmetry_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/vectors/images/sphx_glr_glass_symmetry_003.png
         :alt: PdNiP Signal
         :srcset: /examples/vectors/images/sphx_glr_glass_symmetry_003.png
         :class: sphx-glr-multi-img


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.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (1 minutes 27.050 seconds)


.. _sphx_glr_download_examples_vectors_glass_symmetry.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: glass_symmetry.ipynb <glass_symmetry.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: glass_symmetry.py <glass_symmetry.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: glass_symmetry.zip <glass_symmetry.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_